1. Examine the function to get critical ppints and (if it exists) the point of inflection.

2. I've found a point of inflection with a horizontal tangent at

Therefore

- the function is increasing monotically and must have an increasing inverse function.

- the function can be re-written as

Expand this term and compare it with original term of the function. You'll get a = 1000.

3. Swap the x and y variables in the equation of the function to get the inverse:

Solve for y. I've got: